Question

State the two Kirchhoff’s rules used in electric networks. How are these rules justified?

Answer 1

Kirchhoff’s first rule: In any electrical network, the algebraic sum of currents meeting at a junction is always zero

$\sum I=0$ In the junction below, let $I_1$,$I_2$,$I_3$,$I_4$ and $I_5$ be the current in the conductors with directions as shown in the figure below $I_5$ and $I_3$ are the currents which enter and currents $I_1$ , $I_2$ and $I_4$ leave

According to the Kirchhoff’s law, we have

$(-I_1)$ + $(-I_2)$+ $(-I_3)$+ $(-I_4)$+ $I_5$=0

Or,$I{}_1$+ $I{}_2$+ $I{}_4$= $I{}_3$+ $I{}_5$

Thus, at any junction of several circuit elements, the sum of currents entering the junction must equal the sum of currents leaving it. This is a consequence of charge conservation and the assumption that currents are steady, i.e. no charge piles up at the junction.

Kirchhoff’s second rule: The algebraic sum of changes in potential around any closed loop involving resistors and cells in the loop is zero.

OR

The algebraic sum of the e.m.f. in any loop of a circuit is equal to the algebraic sum of the products of currents and resistances in it

Mathematically, the loop rule may be expressed as $\sum E=\sum IR$